Technical Note: Synthetic Division of the Future Value of a Cash Flow Stream

Abstract

Viewing the future value of a cash flow stream as a polynomial in the compounding factor (being one plus the interest rate), this article uses Ruffini's rule in the synthetic division of a polynomial to provide insight linking several discounted cash flow analysis concepts. We use the polynomial remainder theorem to relate the concepts of divisor, quotient, and remainder to concepts in cash flow analysis—future value, present value, interest rate, account balance, and internal rate(s) of return—establishing a remainder theorem for the future value of a cash flow. Our exposition suggests that future value analysis is perhaps more direct and mathematically more transparent than attention paid to examining present value. This article extends previous work on the resolution of multiple rates of return when the interest rate used in our analysis equals an internal rate of return of the cash flow.